Discontinuous Hamiltonian Finite Element Method for Bilinear Poisson Brackets

Y. Xu, Jacobus J.W. van der Vegt, Onno Bokhove

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    Abstract

    We develop a Hamiltonian discontinuous finite element discretization of a generalized Hamiltonian system for linear hyperbolic systems, which includes the rotating shallow water equations, the acoustic and Maxwell equations. These equations have a Hamiltonian structure with a bilinear Poisson bracket, and as a consequence the phase-space structure, mass and energy are preserved. We discretize the bilinear Poisson bracket in each element with discontinuous elements and introduce numerical fluxes via integration by parts while preserving the skew-symmetry of the bracket. This automatically results in a mass and energy conservative discretization when combined with a symplectic time integration method. For comparison, the discontinuous Galerkin method for this problem is also used. A variety of numerical examples is shown to illustrate the accuracy and capability of the new method.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages34
    Publication statusPublished - Oct 2007

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.LNCS4549/1855
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • METIS-241995
    • EWI-11247
    • IR-64418

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